ODE
\[ 2 y(x) y''(x)=3 y'(x)^2+4 y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.29995 (sec), leaf count = 17
\[\left \{\left \{y(x)\to c_2 \sec ^2(x+2 c_1)\right \}\right \}\]
Maple ✓
cpu = 0.371 (sec), leaf count = 37
\[\left [y \left (x \right ) = \frac {4}{\textit {\_C1}^{2} \left (\sin ^{2}\left (x \right )\right )-\textit {\_C2}^{2} \left (\sin ^{2}\left (x \right )\right )-2 \textit {\_C1} \textit {\_C2} \sin \left (x \right ) \cos \left (x \right )+\textit {\_C2}^{2}}\right ]\] Mathematica raw input
DSolve[2*y[x]*y''[x] == 4*y[x]^2 + 3*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*Sec[x + 2*C[1]]^2}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2+4*y(x)^2, y(x))
Maple raw output
[y(x) = 4/(_C1^2*sin(x)^2-_C2^2*sin(x)^2-2*_C1*_C2*sin(x)*cos(x)+_C2^2)]